Communications in Mathematical Physics

, Volume 155, Issue 2, pp 295–310 | Cite as

Accuracy of mean field approximations for atoms and molecules

  • Volker Bach


We estimate the accuracy of the mean field approximation induced by the Thomas-Fermi potential for the ground state energy of atoms and molecules. Taking the Dirac exchange correction into account, we show the error to be of the formO(Z 5/3−δ )+D for any δ<2/231 as the total nuclear chargeZ becomes large.D is an electrostatic energy of the difference density that measures the deviation of the mean field groud state from self-consistency.


Neural Network Statistical Physic Complex System State Energy Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Volker Bach
    • 1
  1. 1.Fachbereich Mathematik MA 7-2Technische Universität BerlinBerlinGermany

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